1.) The phosphate buffer system is very important for maintaining the pH of the cytoplasm of all cells. Phosphoric acid is a triprotic acid; however, the relevant equilibrium in the biologically useful, neutral range, with pK_a of 6.86 , is that of dihydrogen phosphate and monophosphate ions (data from Table 2.6)

Using the Henderson-Hasselbalch equation, calculate the pH of a solution containing 0.042 M $NaH_2PO_4$ and 0.058 $Na_2HPO_4$

Solution

The acid (HA) in this mixture is $H_2PO_4^-$ , and the conjugate base (A^-) is $HPO_4^{-2}$

Substituting these values into the Henderson-Hasselbalch equation:

2.) An undergraduate student is making 300 mL of 1 M potassium phosphate buffer solution with a pH = 6.96 using 1 M $KH_2PO_4$ and 1 M $K_2HPO_4$ . How many milliliters of 1 M $KH_2PO_4$ will be needed to make this solution?

• pK_a $H_2PO_4^-$ = 7.21

   

Solution

Entering the known values into the Henderson-Hasselbalch equation gives:

So we need to solve for the "mole ratio", aka the $\frac{[A^-]}{[HA]}$ part.

Take the anti-log of both sides,

Next we need to find the total mols in solution. It was given as 300 mL of 1 M solution.

Since we are interested in the amount of $KH_2PO_4$ we will now write the ratio as :

Now we just solve for $X\cdot\ mols$ , notice how we can take out a "1 X" from the right side of the equation.

Finally, we only need to convert mols back into mL using the molarity/concentration provided.